Rectangle ABCD is similar to rectangle WXYZ. If the area of rectangle ABCD is 90 square inches. AD is 10 inches,

and XY is 5 inches, what is the area of rectangle WXYZ? Round to the nearest integer.

a

24 square inches

b.

34 square inches

c

23 square inches

d.

45 square inches

Answer: The answer is option C: 23 square inches

Step-by-step explanation: The two rectangles are given as

ABCD with area of 90 and one side equals 10. That means the other side measures

Area = L x W

90 = 10 x W

90/10 = W

W = 9.

The second rectangle has a side measuring 5 inches and both rectangles have been described as similar. This means there is a common ratio between all sides of both figures.

If AB in rectangle 1 equals 10 inches, and XY in rectangle 2 equals 5 inches, the ratio of both rectangles is given as

Ratio = 10:5

Ratio = 2:1

Hence for rectangle 2, if line AB equals 9, then line WX equals

2/1 = 9/WX

By cross multiplication we now have

WX = 9/2

WX = 4.5

Therefore, the area of rectangle WXYZ is computed as

Area = L x W

Area = 5 x 4.5

Area = 22.5

Approximately to the nearest integer,

Area ≈ 23 square inches